A255539 -id:A255539 - cp's OEIS frontend

A181528 Number of connected graphs with n edges embeddable into square lattice.

1, 1, 1, 2, 4, 6, 14, 28, 68, 156, 399, 1012, 2732, 7385, 20665, 58377, 168119, 488771

Offset: 0

I. E. Kashuba (kashuba(AT)bitp.kiev.ua), Oct 27 2010

a(n) <= number of connected planar graphs with n edges A046091.

			For n = 3 there are a(3) = 2 graphs: the claw graph, corresponding to a single free polystick, and the 3-path, corresponding to 4 different free polysticks.

Andreas R. Hehn, Series Expansion Methods for Quantum Lattice Models, Doctoral Thesis, ETH Zürich, 2016.

Cf. A046091, A019988 (embeddings, or free polysticks), A255539 (with n nodes, neighbors connected).

Terms a(16)-a(17) from Hehn Table 3.1 and a(0) = 1 added by Andrey Zabolotskiy, Oct 22 2022

A255540 Number of connected digital images in Z^2 (regarding each point as connected to its 8 neighbors) on n points up to isomorphism.

Original entry on oeis.org

1, 1, 2, 6, 15, 51, 173, 681, 2682

Offset: 1

P. Christopher Staecker, Feb 24 2015

Also the number of polyplets (A030222) on n points up to isomorphism of adjacency graphs.

			For n=4 the a(4)=6 images are:
X   X X    X    XX    X     X
X    X    X X   XX   XX   XX
X    X     X         X     X
X

P. C. Staecker, Some enumerations of binary digital images, arXiv 1502.06236 [math.CO], 2015 (see table p. 6).
P. C. Staecker, Digital image enumerations

Cf. A255539.

cp's OEIS Frontend

A181528 Number of connected graphs with n edges embeddable into square lattice.

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